A digital subscriber line (DSL) is a data transmission technology using telephone twisted pairs as transmission medium. xDSL is a combination of the DSL technology, which includes a high-speed digital subscriber line (HDSL), a single-pair high-speed digital subscriber line (SHDSL), and an asymmetrical digital subscriber line (ADSL), and the like. The SHDSL is based on baseband transmission. Other xDSLs are based on passband transmission, use the frequency-division multiplexing technology, and may coexist with a plain old telephone service (POTS) in the same twisted pairs.
With higher frequency bands used by the xDSL based on passband transmission, the crosstalk at high frequency band has become a severe problem. FIG. 1 shows a method for solving the crosstalk problem between xDSLs by using a vectored digital subscriber line (vectored-DSL) technology in the conventional art. In the downlink direction, x indicates N×1 signal vectors sent by a coordinated transceiver device (may be a digital subscriber line access multiplexer (DSLAM)); y indicates signal vectors received by N×1 opposite devices (may be a subscriber-side device); and n indicates N×1 noise vectors. A shared channel is expressed by a channel transmission matrix as follow:
  H  =      [                                        h            11                                                h            12                                    …                                      h                          1              ⁢              M                                                                        h            21                                                h            22                                    …                                      H                          2              ⁢              M                                                            ⋮                          ⋮                          ⋱                          ⋮                                                  h                          N              ⁢                                                          ⁢              1                                                            h                          N              ⁢                                                          ⁢              2                                                …                                      h            NN                                ]  
hij(1≦i≦N, 1≦j≦N) indicates a crosstalk transfer function of pair j to pair i; hii(1≦i≦N) indicates the channel transfer function of pair i; and N indicates the number of pairs, i.e., the number of subscribers. If a vector pre-encoder (represented by W) is introduced in the coordinated transceiver device, the signal vectors received by the opposite device receive are calculated by the following formula:{tilde over (y)}=HWx+n 
If the vector pre-encoder can make HW a diagonal matrix, for example, diag (H), the crosstalk may be eliminated.
Supposing N−1 opposite devices are already online and enter a good crosstalk elimination state, the vector pre-encoder of the coordinated transceiver device may be represented as follows:
      W          N      -      1        =      [                                        W            11                                                W            12                                    …                                      W                          1              ,                              N                -                1                                                                                      W            21                                                W            22                                    …                                      W                          2              ,                              N                -                1                                                                          ⋮                          ⋮                          ⋱                          ⋮                                                  W                                          N                -                1                            ,              1                                                            W                                          N                -                1                            ,              2                                                …                                      W                                          N                -                1                            ,                              N                -                1                                                          ]  
If a first-order filter structure is used, all the diagonal elements are 1. When the Nth opposite device goes online, two steps need to be performed: activating a line and joining a vector group. Before these two steps are performed, the Nth opposite device may generate crosstalk on N−1 online opposite devices, and even cause devices to go offline. Thus, when the Nth opposite device goes online, it should not bring about crosstalk that exceeds the tolerance level of N−1 opposite devices. In addition, the process of going online should be as short as possible. In this case, the vector pre-encoder is as follows:
      W    N    =      [                                        W            11                                                W            12                                    …                                      W                          1              ,                              N                -                1                                                                          W                          1              ,              N                                                                        W            21                                                W            22                                    …                                      W                          2              ,                              N                -                1                                                                          W                          2              ,              N                                                            ⋮                          ⋮                          ⋱                          ⋮                          ⋮                                                  W                                          N                ⁢                                                                  -                1                            ,              1                                                            W                                          N                -                1                            ,              2                                                …                                      W                                          N                -                1                            ,                              N                -                1                                                                          W                                          N                -                1                            ,              N                                                                        W                          N              ,              1                                                            W                          N              ⁢                                                          ,              2                                                …                                      W                          N              ,                              N                -                1                                                                          W                          N              ,              N                                            ]  
Compared with WN-1, WN is added with a row and a column of vectors. The added column of vectors is used to eliminate the crosstalk of the Nth opposite device on N−1 online opposite devices. Thus, to reduce the crosstalk of the Nth opposite device on N−1 online opposite devices quickly, the vectors in the column of N−1 dimensions should be calculated in a short time. In the conventional art, the opposite device needs to transmit a large amount of data back to the coordinated transceiver device. However, the capacity of the feedback channel from the opposite device to the coordinated transceiver device is limited, which prolongs the time required for calculating the vectors in the new added column.